截断调和Bergman空间上的Toeplitz算子

截断调和Bergman空间b_n~2=L_a~2{w,w~2,…,w~n}~v是Hilbert空间L~2的闭子空间.研究了单位圆盘上的截断调和Bergman空间上的Toeplitz算子的乘积问题,完整地刻画了具有有界调和符号的两个Toeplitz算子的有限秩与紧的半换位子或换位子.     

Hardy空间上一类$m$-复对称Toeplitz算子

本文主要研究Toeplitz算子相对于一对置换的共轭算子是2-复对称的充要条件. 首先在经典的Hardy空间上介绍一类被称为一对置换的共轭算子, 其次完整地刻画了在这类共轭算子下Toeplitz算子是2-复对称的结构, 利用Toeplitz算子在Hardy空间的经典正规正交基下的矩阵表示来刻画2-复对称Toeplitz算子. 最后对于Toeplitz算子分别补充前提$f_n=-f_{-n}$和$f_n=f_{-n}$, 得到了更简化的结果. 在第二个前提下, 研究Toeplitz算子的3-复对称性, 得到$T_f$关于$C_{(i,j)}$是3-CSO的结果和是2-CSO相同.     

多圆盘上Hardy空间上的Berezin变换和Toeplitz算子的交换性

,该文讨论多圆盘上Hardy空间上的Toeplitz算子,使用Berezin变换和调和扩张给出两个Toeplitz算子交换的一个充要条件.     

截断调和Bergman空间上Toeplitz算子的代数性质

本文首先讨论调截断和Bergman空间 $b_{n}^{2}$ 上拟齐次函数为符号的Toeplitz算子的有限秩乘积问题,其次考察两个以拟齐次函数为符号的Toeplitz算子的换位子与半换位子的有限秩问题.     

调和Hardy空间上的Toeplitz算子的酉等价性

记H²是单位圆盘D={ξ∈C:|ξ|<1}上的经典Hardy空间.设u和v是内函数且至少其中一个是非常值的,调和Hardy空间H_u,v²定义为H_u,v²=uH²⊕v(H²)^丄=uH²⊕vzH².对任意的x∈H_u,v²,定义H_u,v²上的调和Toeplitz算子T_φx=Q_u,v(φx),其中,Q_u,v:L²→H_u,v²为正交投影.该文刻画了调和Toeplitz算子和对偶截断Toeplitz算子的酉等价性,并给出了两个调和Toeplitz算子可交换的充要条件,调和Toeplitz代数的性质以及T_z的换位子的刻画.最后,该文还得到了...     

多圆盘调和Hardy空间上对偶Toeplitz的代数性质

本文给出多圆盘上的调和Hardy空间的定义, 并且给出多圆盘调和Hardy空间上对偶对偶Toeplitz算子的某些代数性质.     

多重调和Bergman空间上的Toeplitz算子和Hankel算子

完全刻画多重调和Bergman空间上Toeplitz算子和Hankel算子的紧性.运用紧Toeplitz算子这个结果,建立了Toeplitz代数和小Hankel代数的短正合列,推广了单位圆盘上相应的结果.     

Hardy空间上某些解析Toeplitz算子的换位及约化子空间

讨论了Hardy空间上以非退化有界单叶解析函数的幂为符号的解析Toeplitz算子的换位.并且刻划了符号为三个Blaschke因子积的解析Toeplitz算子的约化子空间.     

双圆盘上Hardy空间上Hankel 算子和Toeplitz 算子的交换性

In this paper, we characterize when the Toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condition on the symbols to guarantee TfHg = HgTf.     

Commuting Toeplitz operators with pluriharmonic symbols

By making use of -harmonic function theory, we characterize commuting Toeplitz operators with bounded pluriharmonic symbols on the Bergman space of the unit ball or on the Hardy space of the unit sphere in -dimensional complex space.

     

Toeplitz products with pluriharmonic symbols on the Hardy space over the ball

On the Hardy space over the unit ball in Cn, we consider operators which have the form of a finite sum of products of several Toeplitz operators. We study characterizing problems of when such an operator is compact or of finite rank. Some of our results show higher-dimensional phenomena.     

重调和Hardy空间Toeplitz算子的交换性

本文研究重调和Hardy空间h~2(Ω)上,Toeplitz算子的交换性,给出了h~2(T~2)上一个解析Toeplitz算子与另一个共轭解析Toeplitz算子交换的充分必要条件.     

Commuting Toeplitz operators on the Hardy space of the bidisk

On the Hardy space of the bidisk, we give a necessary and sufficient condition for a bounded symbol of a Toeplitz operator that commutes with another Toeplitz operator whose symbol is a certain type of bounded symbol.     

Positive Toeplitz operators between the pluriharmonic Bergman spaces

We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space b ^p into another b ^q for 1 < p, q < ∞ in terms of certain Carleson and vanishing Carleson measures. This research was supported by KOSEF (R01-2003-000-10243-0) and Korea University Grant.     

Commuting dual Toeplitz operators with pluriharmonic symbols

In this paper we completely characterize commuting dual Toeplitz operators with bounded pluriharmonic symbols on the Bergman space of the unit ball. We show that for φ and ψ pluriharmonic, SφSψ=Sψφ on only in the trivial case. Here the trivial case is φ or holomorphic.     

Schatten-Herz type positive Toeplitz operators on pluriharmonic Bergman spaces

Recently, Schatten-Herz type Toeplitz operators have been studied on the Bergman spaces and the harmonic Bergman spaces. Motivated these results, we study characterizations of positive Toeplitz operators of Schatten-Herz type in terms of averaging functions and Berezin transforms of symbol functions on the ball of pluriharmonic Bergman spaces.     

Compact Toeplitz operators on the Segal-Bargmann space

In this note, we show that Miao and Zheng's characterization of compact operators on the Bergman space of the unit disk that are finite sums of finite products of Toeplitz operators (with each one of the symbols belonging to BT) also holds for the Segal-Bargmann space of Cn.